A general theory of neutron scattering (elastic and inelastic) is presented
. It is applicable to the whole domain of slow neutrons and includes, as li
miting cases, existing theories for thermal and cold neutrons and for the e
lastic scattering of UCN. A new expression for the inelastic scattering cro
ss section for UCN is proposed. It differs from the one usually used by con
sistently taking into account re-scattering processes. Evidence for slight
heating and cooling of UCN is given. (C) 2000 Elsevier Science B.V. All rig
hts reserved.